The hyper-zagreb index of graph operations
01 May 2013-Iranian journal of mathematical chemistry (IRANIAN JOURNAL OF MATHEMATICAL CHEMISTRY)-Vol. 4, Iss: 2, pp 213-220
TL;DR: In this article, the Hyper Zagreb index of Cartesian product, composition, join, and disjunction of graphs is computed for simple connected graphs, where the distance between vertices is defined as the degree of vertices.
Abstract: Let G be a simple connected graph. The first and second Zagreb indices have been introduced as vV(G) (v)2 M1(G) degG and M2(G) uvE(G)degG(u)degG(v) , respectively, where degG v(degG u) is the degree of vertex v (u) . In this paper, we define a new distance-based named HyperZagreb as e uv E(G) . (v))2 HM(G) (degG(u) degG In this paper, the HyperZagreb index of the Cartesian product, composition, join and disjunction of graphs are computed.
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